Journals and Posts

My great grandmother's name was Susan Hamilton.
She married my great grandfather John Leich in Brooklyn NY in the 1870s.
Susan was born in Waterford New York in the mid 1800s.
Her father was born in England and her mother in Ireland. I believe they immigrated to the United States shortly before Susan's birth.
I have Susan's date of birth, the names of her siblings and her parents' names.

My question is, "Where should I best go with this information to determine if Susan Hamilton and consequently myself are related to Alexander Hamilton?